A Primal-Dual Algorithm for Higher-Order Multilabel Markov Random Fields
2014 IEEE Conference on Computer Vision and Pattern Recognition
Graph cuts method such as α-expansion  and fusion moves  have been successful at solving many optimization problems in computer vision. Higher-order Markov Random Fields (MRF's), which are important for numerous applications, have proven to be very difficult, especially for multilabel MRF's (i.e. more than 2 labels). In this paper we propose a new primal-dual energy minimization method for arbitrary higher-order multilabel MRF's. Primal-dual methods provide guaranteed approximation
... approximation bounds, and can exploit information in the dual variables to improve their efficiency. Our algorithm generalizes the PD3  technique for first-order MRFs, and relies on a variant of max-flow that can exactly optimize certain higher-order binary MRF's  . We provide approximation bounds similar to PD3 , and the method is fast in practice. It can optimize non-submodular MRF's, and additionally can incorporate problem-specific knowledge in the form of fusion proposals. We compare experimentally against the existing approaches that can efficiently handle these difficult energy functions [6, 10, 11] . For higher-order denoising and stereo MRF's, we produce lower energy while running significantly faster.